Same as other one. How would I solve derivative simplifying results?
g(x)=√2x^4+x^2+1
r(x) 2x^2-5x^-12/x-4
m(x) = -5(x^4+3)^8
k(x)=2x/x^2+2
For g(x), I'm taking that to be $\displaystyle \sqrt{2x^4+x^2+1}$ Let u = $\displaystyle 2x^4+x^2+1$ and let $\displaystyle \frac{du}{dx}=8x^3+2x$ So g(x) can now be written as $\displaystyle \sqrt{u}$ Now taking the derivative, you get $\displaystyle g'(x)=\frac{1}{2\sqrt{u}}*\frac{du}{dx}$. Now back substitute everything in. Does this method make sense? It can be a lot to take in.
For r(x) and k(x), just use the quotient rule.
$\displaystyle \frac{d}{dx}\frac{u}{v}=\frac{vu'-uv'}{v^2}$
All of the questions use the powerful CHAIN RULE. Make sure to learn that solidly.